x^2-7=x-6x-7

Solution for x^2-7=x-6x-7 equation:

x^2-7=x-6x-7

We move all terms to the left:

x^2-7-(x-6x-7)=0

We add all the numbers together, and all the variables

x^2-(-5x-7)-7=0

We get rid of parentheses

x^2+5x+7-7=0

We add all the numbers together, and all the variables

x^2+5x=0

a = 1; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*1}=\frac{0}{2}
=0
$